Fractions and Pizza

We were starting some inquiring into fractions in Year 6. We began our tuning in by looking at a Youtube clip:

This is the image to select when you search for "Fractions in real life"

and here is the link....

http://www.youtube.com/watch?v=8hmb0FyGe4Y

As with any discussion of fractions, the conversation turned to pizza. We all agreed that pizza was a poor example because of that pizza guy who cuts the pieces so carelessly that you always end up with some pieces that are obviously smaller than the others. 

How can this be a good example of fractions, we asked ourselves.

The conversation then moved on to the things that we already knew about fractions.

Here's what we knew:

• fractions are used to measure
• fractions represent equal parts of a whole (unlike the pizza above)
• the top number can be bigger than the bottom number
• fractions are related to decimals and percentages
• they are a way of dividing things up
• the bigger the denominator, the smaller the fraction

I wanted to explore this last idea a bit further, so I put the following list of fractions up on the smartboard:

1/2   1/3   1/4    1/5    1/6    1/7

We talked about what was happening and how, if the numerator was the same, the smallest fraction was the one with the biggest denominator.

"Yes, so it is," I agreed. "But why?"

"Well," replied one Wise and Wonderful student....

"You can't make the pizza bigger, so the pieces must be getting smaller."